LABELLING TRIANGLES OPPOSITE ADJACENT HYPOTENUSE

Use the following triangles to determine the trig ratios below. Simplify all fractions, rationalize and simplify all radicals, and convert all decimal answers to fractions.

Problem 1 :

labelling-triangles-opp-adj-hypo-q1

Solution :

sin A = OppositeHypotenuse= BCAC= 315615sin A= 12cos C = AdjacentHypotenuse= BCAC= 315615cos C= 12tan C = OppositeAdjacent= ABBC= 95315= 3515= 355 × 3= 355 × 3= 33= 3 × 33tan C= 31

Problem 2 :

labelling-triangles-opp-adj-hypo-q2

Solution :

sin F = OppositeHypotenuse= DEDF= 71052= 710 × 25= 1450sin F= 725cos D = AdjacentHypotenuse= DEDF= 71052= 710 × 25= 1450cos D= 725cos F = AdjacentHypotenuse= EFDF= 12552= 125 × 25cos F= 2425

Problem 3 :

labelling-triangles-opp-adj-hypo-q3

Solution :

sin H = OppositeHypotenuse= GIGH=2.17.5= 2.17.5 × 1010= 2175sin H= 725cos G = AdjacentHypotenuse= GIGH=2.17.5= 2.17.5 × 1010= 2175cos G= 725tan H =OppositeAdjacent= GIHI=2.17.2= 2.17.2 × 1010= 2172tan H = 724

Problem 4 :

labelling-triangles-opp-adj-hypo-q4

Solution :

sin J = OppositeHypotenuse= KLJL= 39sin J = 13cos L = AdjacentHypotenuse= KLJL= 39cos L= 13tan L = OppositeAdjacent= KJKL= 623tan L= 221

Problem 5 :

labelling-triangles-opp-adj-hypo-q5

Solution :

sin M = OppositeHypotenuse= NOMO=651310= 65 × 1013= 6065sin M= 1213cos O = AdjacentHypotenuse= NOMO=651310= 65 × 1013= 6065cos O = 1213tan M =OppositeAdjacent= NOMN=6512= 65 × 21= 125tan M= 125

Problem 6 :

labelling-triangles-opp-adj-hypo-q6

Solution :

sin P = OppositeHypotenuse= RQPR=2451sin P= 817tan P =OppositeAdjacent= RQPQ=2445tan P = 815tan R =OppositeAdjacent= PQRQ=4524tan R = 158

Problem 7 :

labelling-triangles-opp-adj-hypo-q7

Solution :

sin S = OppositeHypotenuse= UTST=2250.11=2250.1 × 101 × 10 = 225110= 225 × 101= 2025= 45sin S = 45sin T = OppositeHypotenuse= SUST=0.0610.11=0.06 × 1001 × 1000.1 × 101 × 10 = 6100110= 6100 × 101= 60100sin T= 35tan T =OppositeAdjacent= SUUT=0.061225=0.06 × 1001 × 100225 = 6100225= 6100 × 252= 150200tan T= 34

Problem 8 :

labelling-triangles-opp-adj-hypo-q8

Solution :

cos V = AdjacentHypotenuse= WXVW=66123cos V= 22cos W = AdjacentHypotenuse= WXVW=66123cos W= 22tan W =OppositeAdjacent= VXWX=25466= 93= 33tan W= 11

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